On Power Allocation For Distributed Detection With Correlated Observations And Linear Fusion

Keywords

coherent reception; correlated observations; Distributed detection; linear fusion; modified deflection coefficient; multiple access channel; orthogonal channels; parallel access channel; power allocation

Abstract

We consider a binary hypothesis testing problem in a wireless sensor network, where a fusion center (FC) makes a final decision about the underlying hypothesis. We assume under hypothesis H0, sensors' observations are uncorrelated and identically distributed Gaussian, however, under H1 they are correlated and nonidentically distributed Gaussian and sensors are unaware of this correlation when making decisions. Sensors send their local binary decisions over power constrained fading channels. We consider both parallel access channel (PAC) and multiple access channel (MAC) models. To obtain the detection statistic in PAC, we assume that the FC utilizes a linear fusion rule, which linearly combines the signals received from all sensors, while in MAC, the signal received at the FC is naturally the coherent sum of the transmitted signals. For both PAC and MAC, we derive modified deflection coefficient (MDC) of the detection statistic at the FC with coherent reception. Choosing MDC as the detection performance metric, we formulate several constrained transmit power optimization problems. In these problems, MDC is the objective function to be maximized and there are three different sets of transmit power constraints: total power constraint, individual and total power constraints, and individual power constraints only. We refer to the solutions of these constrained optimization problems as MDC-based transmit power allocation. When analytical solutions to these constrained optimization problems are elusive, we discuss how these problems can be converted to convex ones. Our results show that, compared with equal power allocation, detection performance improvement provided by our proposed MDC-based power allocation is more significant in MAC. We quantify the improvement in terms of several factors, including the degree of correlation among sensors' observations, reliability of local decisions (local detection performance indices), communication channel properties, and the type of transmit power constraint. We also study how the power allocation among sensors varies as these factors change.

Publication Date

9-1-2018

Publication Title

IEEE Transactions on Vehicular Technology

Volume

67

Issue

9

Number of Pages

8396-8410

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/TVT.2018.2847300

Socpus ID

85048521735 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85048521735

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